Cross-domain temperament merging: Difference between revisions

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From this, we can make some helpful statements:

''For a comma-merge'', because the output temperament deals with every comma, then its domain basis must be capable of supporting this: specifically, it must include every basis element from any of the input temperaments' domain bases. Think of it this way: for any given temperament, its domain basis elements are the building blocks for its commas, and so in order to express every comma in the merged temperament, we will need every input temperament's building blocks gathered in one place. In other words, we must find the merge of all the input domain bases.

''For a comma-merge'', because the output temperament deals with every comma, then its domain basis must be capable of supporting this: specifically, it must include every [[basis element]] from any of the input temperaments' domain bases. Think of it this way: for any given temperament, its domain basis elements are the building blocks for its commas, and so in order to express every comma in the merged temperament, we will need every input temperament's building blocks gathered in one place. In other words, we must find the merge of all the input domain bases.

''For a map-merge'', then, because the output temperament will deal only with tempered commas shared by every input temperament, then its domain basis only needs to include the basis elements that are present in all of the input domain bases. Here's why: a comma built using a basis element that isn't shared by all input temperaments couldn't even be ''built'' in all input temperaments, let alone tempered out by all of them. And so, to build the set of commas that are tempered out by all temperaments, we only need the building blocks that can be found in all of them. In mathematical terms, we must find the intersection of the input domain bases.

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 From this, we can make some helpful statements:
-''For a comma-merge'', because the output temperament deals with every comma, then its domain basis must be capable of supporting this: specifically, it must include every basis element from any of the input temperaments' domain bases. Think of it this way: for any given temperament, its domain basis elements are the building blocks for its commas, and so in order to express every comma in the merged temperament, we will need every input temperament's building blocks gathered in one place. In other words, we must find the merge of all the input domain bases.
+''For a comma-merge'', because the output temperament deals with every comma, then its domain basis must be capable of supporting this: specifically, it must include every [[basis element]] from any of the input temperaments' domain bases. Think of it this way: for any given temperament, its domain basis elements are the building blocks for its commas, and so in order to express every comma in the merged temperament, we will need every input temperament's building blocks gathered in one place. In other words, we must find the merge of all the input domain bases.
 ''For a map-merge'', then, because the output temperament will deal only with tempered commas shared by every input temperament, then its domain basis only needs to include the basis elements that are present in all of the input domain bases. Here's why: a comma built using a basis element that isn't shared by all input temperaments couldn't even be ''built'' in all input temperaments, let alone tempered out by all of them. And so, to build the set of commas that are tempered out by all temperaments, we only need the building blocks that can be found in all of them. In mathematical terms, we must find the intersection of the input domain bases.